Chapter 12, Problem 7STP

To determine

To find the lengths of diagonals of kite.

Answer to Problem 7STP

  $8$ inch, $24$ inch

Explanation of Solution

Given:

Length of one diagonal of the kite is three times the length of the other diagonal.

Area of kite $=96$ square inches

Formula used:

Area of a kite $=\frac{d_1{d}_2}{2}$

Where $d_1=$ length of one diagonal

  $d_2=$ length of the other diagonal

Calculation:

Let $d_1$ represent the length of one diagonal, then $3d_1$ represent the length of the other diagonal.

Using the area of the kite to find the value of $d_1$ .

Area of a kite $=\frac{d_1{d}_2}{2}$

  $\Rightarrow 96=\frac{d_1\cdot 3d_1}{2}$

  $\Rightarrow 96\cdot 2=3d_1{}^2$

  $\Rightarrow 192=3d_1{}^2$

  $\Rightarrow 64=d_1{}^2$

[Dividing both sides by $3$ ]

  $\Rightarrow \sqrt{64}=d_1$

  $\Rightarrow 8=d_1$

Now, $d_2=3d_1$

  $\Rightarrow d_2=3\times 8=24$

So, the length of one diagonal is $8$ inch and the other diagonal is $24$ inch.

Conclusion:

Therefore, the length of one diagonal is $8$ inch and the other diagonal is $24$ inch.