CUET CUET General Test 2024 - In a square, lengths of the diagonals are (4k + 6) cm and (7k − 3) cm. The area of the square (in cm²) is: | PYQs + Solutions

CUET General Test 2024

Geometry

Quadrilaterals

Medium

In a square, lengths of the diagonals are $(4k + 6)$ cm and $(7k − 3)$ cm. The area of the square (in cm²) is:

144

162

169

172

Correct Option: 2

Since the diagonals of a square are equal, we can set the two expressions for the diagonals equal to each other:

4k + 6 = 7k - 3

Now, solve for

k

6 + 3 = 7k - 4k

9 = 3k

k = 3

Now, substitute

k

back into one of the diagonal expressions to find the length of the diagonal:

Diagonal =

4(3) + 6 = 12 + 6 = 18

cm.

The area of the square can be calculated using the formula for the area in terms of the diagonal:

Area =

\frac{d^2}{2}

, where

d

is the length of the diagonal.

Area =

\frac{18^2}{2} = \frac{324}{2} = 162

cm².

Thus, the area of the square is 162 cm².