In the adjoining diagram, AB = x cm, BC = y cm and x - y = 7 cm. Area of △ ABC = 30 cm 2 . The length of AC is : 1. 10 cm 2. 12 cm 3. 13 cm 4. 15 cm

By formula, Area of triangle = ⇒ 30 = ⇒ 30 = ⇒ 30 = ⇒ xy = 60 ........(1) Given, ⇒ x - y = 7 ⇒ x = 7 + y ........(2) Substituting value of x from equation (2) in (1), we get : ⇒ (7 + y)y = 60 ⇒ 7y + y 2 = 60 ⇒ y 2 + 7y - 60 = 0 ⇒ y 2 + 12y - 5y - 60 = 0 ⇒ y(y + 12) - 5(y + 12) = 0 ⇒ (y - 5)(y + 12) = 0 ⇒ y - 5 = 0 or y + 12 = 0 ⇒ y = 5 or y = -12. Since, side cannot be negative, ∴ y = 5 cm. Substituting value of y in equation (2), we get : ⇒ x = 7 + y = 7 + 5 = 12 cm. In right angle triangle ABC, By pythagoras theorem, ⇒ AC 2 = AB 2 + BC 2 ⇒ AC 2 = x 2 + y 2 ⇒ AC 2 = 12 2 + 5 2 ⇒ AC 2 = 144 + 25 ⇒ AC 2 = 169 ⇒ AC = = 13 cm. Hence, Option 3 is the correct option.

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In solving a quadratic equation, one of the values of the variables x is 233.356. The solution rounded to two significant figures is :
233.36
233.35
233.3
230

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If p, q, and r are in continued proportion, then :
p : q = p : r
q : r = p² : q²
p : q² = r : p²
p : r = p² : q²

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The ratio of diameter to height of a Borosil cylindrical glass is 3 : 5. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is :
120π
60π
30π
18π

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Mathematics

In the adjoining diagram, AB = x cm, BC = y cm and x - y = 7 cm. Area of △ ABC = 30 cm². The length of AC is :
10 cm
12 cm
13 cm
15 cm

Quadratic Equations

Related Questions

In solving a quadratic equation, one of the values of the variables x is 233.356. The solution rounded to two significant figures is :
233.36
233.35
233.3
230

If p, q, and r are in continued proportion, then :
p : q = p : r
q : r = p² : q²
p : q² = r : p²
p : r = p² : q²

The ratio of diameter to height of a Borosil cylindrical glass is 3 : 5. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is :
120π
60π
30π
18π

Mathematics

In the adjoining diagram, AB = x cm, BC = y cm and x - y = 7 cm. Area of △ ABC = 30 cm2. The length of AC is :10 cm12 cm13 cm15 cm

Quadratic Equations

Related Questions

In solving a quadratic equation, one of the values of the variables x is 233.356. The solution rounded to two significant figures is :233.36233.35233.3230

If p, q, and r are in continued proportion, then :p : q = p : rq : r = p2 : q2p : q2 = r : p2p : r = p2 : q2

The ratio of diameter to height of a Borosil cylindrical glass is 3 : 5. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is :120π60π30π18π

In the adjoining diagram, AB = x cm, BC = y cm and x - y = 7 cm. Area of △ ABC = 30 cm². The length of AC is :
10 cm
12 cm
13 cm
15 cm

In solving a quadratic equation, one of the values of the variables x is 233.356. The solution rounded to two significant figures is :
233.36
233.35
233.3
230

If p, q, and r are in continued proportion, then :
p : q = p : r
q : r = p² : q²
p : q² = r : p²
p : r = p² : q²

The ratio of diameter to height of a Borosil cylindrical glass is 3 : 5. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is :
120π
60π
30π
18π