Question

Find the length of the diagonal of a rectangle whose sides measure 15cm and 20cm.

Answer 1

As we each angle of rectangle makes 90°

So,

Let AB=15cm
BC=20cm


Let diagonal be hypotenuse(AC)

So , using Pythagoras theorem

AB²+BC²=AC²
15²+20²=AC²
225+400=AC²
625=AC²
25=AC

25cm is diagnol

Answer 2

Hey There!

Sheena Here!

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Before I give the solution Let me tell you what is a Rectangle.

=> A Rectangle is a 4 sided polygon i.e A Quadrilateral.

=> The Measure of its opposite sides are same.

=> The Sides of the rectangle are known as Length and Breadth.

=> Measure of its all the 4 angles is 90 degree.

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Coming to your question!

Question: Find the length of the diagonal of a rectangle whose sides measure 15cm and 20cm.

Solution:

We know that a rectangle as 2 different measures i.e measure of the length and the breadth.

We also know that the angle formed between the length and the breadth is 90 degree.

So, when we draw a diagonal in the rectangle, It forms 2 right-angled Triangles.

The largest side of the triangle is know as the hypotenuse.

=> We will find the Hypotenuse (Diagonal) through Pythagoras Theorem.

Pythagoras Theorem: $a^{2} + b^2 = c^2$

∴ $15^{2} + 20^{2}$ = $c^{2}$

∴ 225 + 400 = $c^{2}$

∴ 625 = $c^{2}$

∴ c = $\sqrt{625}$

∴ c = 25 cm

As the Hypotenuse (c) is the diagonal so the measure of the diagonal is 25 cm.

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Hope this helps!

Thanks!