Question

If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.
A) 110
B) 120
C) 130
D) 140

Answer 1

Let L be the length and b be the breadth
Given:
Diagonal = 17 cm
root ((L^2) + (b^2)) = 17

squaring both sides:

(L^2) + (b^2)= 17^2
(L^2) + (b^2)= 289 ***eqn a

Given:
Perimeter =46 cm
2(L + b) = 46
(L + b) = 23 ***eqn b

we have:
(L + b)^2 = (L^2) + 2Lb + (b^2)

Rearranging:
(L + b)^2 = (L^2) + (b^2) + 2Lb

Substituting values from eqn a and eqn b:

23^2 = 289 + 2Lb
529 = 289 + 2Lb
2Lb = 529-289
2Lb = 240
Lb = 120
Area = 120

The answer is (B) 120