Question

A kite of area 40 m squarehas one diagonal 2 m longer than the other. Find the length of the diagonal

Answer 1

• Length of diagonal 1: 8 meters
• Length of diagonal 2: 10 meters

Explanation:

Let d1 be the first diagonal and d2 be the second diagonal.

Given

Area = 40 square meters

And one diagonal is 2 meter longer than other

`d_2 = d_1+2`

The formula for area of kite is;

`Area = (1)/(2) * d_1 * d_2`

Putting the known values

`40 = (1)/(2) * d_1 * (d_1+2)\\80 = (d_1)^2+2d_1\\d_1^2 +2d_1-80 = 0\\`

The expression is a quadratic polynomial

Factorizing

`d_1^2 + 10d_1-8d_1-80 = 0\\d_1(d_1+10)-8(d_1+10) = 0\\(d_1+10)(d_1-8) = 0\\d_1 + 10 = 0\\d_1 = -10\\d_1-8 = 0\\d_1 = 8`

As the value of length cannot be negative so discarding the negative value

`d_1 = 8d_2 = d_1+2 = 8+2 =10`

Hence,

• Length of diagonal 1: 8 meters
• Length of diagonal 2: 10 meters