Question

Find the length of the diagonal of a
rectangle whose breadth and length are 8 cm and 15 cm, respectively.​

Answer 1

Step-by-step explanation:

Find the length of the diagonal of a rectangle whose sides are 15 cm and 8 cm. Get the ... Length=15cmand breadth =8cm

Answer 2

ɢɪᴠᴇɴ:-

• Length of rectangle is 15 cm
• Breath of rectangle is 8 cm

ᴛᴏ ғɪɴᴅ:-

• The length of the diagonal of rectangle.

ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

Let the length of the diagonal of the rectangle be x cm.

As we know that,

• The diagonal of the rectangle, cuts it into two right triangles.

Here, the hypotenuse of the triangle is the diagonal of the rectangle.

In ΔABD, ∠A = 90°.

Using Pythagoras Theorem ;

BD² = AD² + AB²

$\begin{lgathered}:\implies x^2= (8)^2 + (15)^2\\\end{lgathered}$

$\begin{lgathered}:\implies x^2 = 64 + 225 \\\end{lgathered}$

$\begin{lgathered}:\implies x^2= 289\\\end{lgathered}$

$\begin{lgathered}:\implies x = ± \sqrt{289}\end{lgathered}$

$\begin{lgathered}:\implies x = ± \ 17\end{lgathered}$

Since, length can't be negative.

$\begin{lgathered}:\implies{\boxed{\frak{\purple{BD = x = 17 \;cm}}}}\;\bigstar\\ \\\end{lgathered}$

Hence, the diagonal of the rectangle is 17 cm.

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