Question

A kite of area 40m has one diagonal 2 m longer than the other.
Find the lengths of the diagonals.​

Answer 1

Answer:

The length of the diagonals are 8cm and 10cm

Step-by-step explanation:

Let the length of the shorter diagonal be x cm. Therefore, the length of the other diagonal is x+2 cm.

Area of a kite = $\frac{1}{2}$ ×(product of diagonals)

∴ 40 =$\frac{(x)(x+2)}{2}$

80 = $x^{2}$ +2$x$

Now, a quadratic equation can be used to find the answer.

$x^{2} + 2x-80 = 0$

$x^{2} +10x-8x-80 = 0$

$x(x+10) - 8(x+10) = 0$

$(x+8)(x-10) = 0$

$x = -10$ or $x = 8$

Since this is a diagonal, the minus value cannot be taken. So, the lengths of the diagonals = 8 cm & 10 cm (=8+2)