Each of equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.

Each of equal sides of an isosceles triangle is 4 cm greater than its height. Let `h` be the height of the triangle. Equal sides: AB = AC = h + 4 Base: BC = 24 cm In Δ ABD and Δ ACD, AD = AD [∵ Common Side] ∠ ADB = ∠ ADC [∵ Both are 90°] AB = AC [∵ Δ ABC is isosceles] ∴ Δ ABD ≅ Δ ACD [RHS axiom] ∴ BD = CD [C.P.C.T] ∴ BD = CD = = = 12 cm By using the Pythagoras theorem in Δ ABD, BD 2 + AD 2 = AB 2 ⇒ 12 2 + h 2 = (h + 4) 2 ⇒ 144 + h 2 = h 2 + 4 2 + 2 x h x 4 ⇒ 144 + = + 16 + 8h ⇒ 144 - 16 = 8h ⇒ 128 = 8h ⇒ h = ⇒ h = 16 cm ⇒ a = h + 4 = 16 + 4 = 20 cm Perimeter of triangle = Sum of all sides = AB + AC + BC = (20 + 20 + 24) cm = 64 cm Area of triangle = x base x height = x 24 x 16 = 12 x 16 = 192 cm 2 Hence, the perimeter is 64 cm and the area is 192 cm 2 .

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

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The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :
(i) its area.
(ii) altitude of the triangle corresponding to its largest side.
(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.

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Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

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In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm². Find the sides of the triangle.

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Mathematics

Each of equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.

Mensuration

Related Questions

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :
(i) its area.
(ii) altitude of the triangle corresponding to its largest side.
(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm². Find the sides of the triangle.

Mathematics

Each of equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.

Mensuration

Related Questions

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m2 is ₹ 49,572; find its base and height.

The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :(i) its area.(ii) altitude of the triangle corresponding to its largest side.(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm2. Find the sides of the triangle.

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :
(i) its area.
(ii) altitude of the triangle corresponding to its largest side.
(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.

In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm². Find the sides of the triangle.