Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Mensuration: 2D

Question:

The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm2. What is the perimeter (in cm) of the triangle?

Options:

40

49

36

56

Correct Answer:

56

Explanation:

Let one side of triangle = a cm 

Other perpendicular side = a - 17

Area of right angled triangle = \(\frac{1}{2}\) × a × (17 - a) = 84

= a2 – 17a - 168 = 0

= a2 – 24a + 7a - 168 = 0

= a(a - 24) +7 (a - 24) = 0

= (a +7) (a - 24) = 0

= a = 24

Thus, H2 = (24)2 + (7)2 = 625

H = 25

Sides of triangle are a = 24 cm,

 a - 17 = 7 cm 

H = 25 cm

Perimeter of triangle = 24 + 7 + 25 = 56 cm