Question

9) Find the perimeter of a rectangle whose length is 15 m and the
diagonal is 17 m.​

Answer 1

Answer :

• The perimeter of rectangle is 48m.

Step-by-step explanation ::

To Find :-

• The perimeter of rectangle

Solution :-

Given that,

• Length of rectangle = 15m
• Diagonal of rectangle = 17m

First we need to find out the breadth of rectangle, As Perimeter of rectangle= 2 ( Length+ Breadth )

Therefore, the breadth of rectangle is,

We can find out the breadth by using the formula of diagonal of Rectangle,

$\bf{ \underline{Diagonal \: of \: rectangle} = \sqrt{{l}^{2} + {b}^{2}}}$

$\longmapsto \: \sf{\sqrt{{l}^{2} + {b}^{2}} = {17}^{2}} \\ \\ \\ \longmapsto \: \sf{\sqrt{{15}^{2} + {b}^{2} = {17}^{2}}} \\ \\ \longmapsto \: \sf{225+ {b}^{2} = 289} \\ \\ \\ \longmapsto \: \sf{{b}^{2} = 289 - 225} \\ \\ \\ \longmapsto \: \sf{{b}^{2} = 64} \\ \\ \\ \longmapsto \: \sf{{b}^{2} = \sqrt{64}} \\ \\ \\ \longmapsto \: \sf{b = 8}$

Therefore, the breadth of rectangle is 8m.

Now, the perimeter of rectangle,

According the question,

As we know that,

$\bf{ \underline{Perimeter \: of \: rectangle} = 2(l+b)}$

Where,

• l = Length
• b = Breadth

$\sf{ \longmapsto \: Perimeter = 2(l+b)} \\ \\ \\ \sf{ \longmapsto \: Perimeter = 2(15+8)} \\ \\ \\ \sf{ \longmapsto \: Perimeter = 2(23)} \\ \\ \\ \sf{ \longmapsto \: Perimeter = 2 \times 23} \\ \\ \\ \bf{ \longmapsto \: Perimeter = 46}$

• The perimeter of rectangle is 46m.