Question

The length of a rectangle is 12 cm and each of its diagonal measures 15 cm. Find its breadth.​

Answer 1

Answer:

The diagonal, length and breadth of a rectangle form a right angled triangle with diagonal as the hypotenuse.

Therefore,

l^2 + b^2 = d^2

(12)^2 + b^2 = (15)^2

b^2 = 81

b = 9 cm

Answer 2

Step-by-step explanation:

Given :

• Length of the rectangle is 12 cm.
• Measure of it's diagonal is 15 cm.

To Find :

• Measure of it's breadth.

Solution :

✨If we draw the diagram so we can see it's forming a right angles triangle.

By applying Pythagoras Theorem,

♣ Let the breadth be x cm.

$\displaystyle{ \mathfrak{ \leadsto \: {p}^{2} + {b}^{2} = {h}^{2} }}$

$\displaystyle{ \mathfrak{ \leadsto \: { \sf{x}}^{2} + {12}^{2} = {15}^{2} }}$

$\displaystyle{ \mathfrak{ \leadsto \: { \sf{x}}^{2} + 144 = 225 }}$

$\displaystyle{ \mathfrak{ \leadsto \: { \sf{x}}^{2} = 225 - 144}}$

$\displaystyle{ \mathfrak{ \leadsto \: { \sf{x}}^{2} = 81}}$

$\displaystyle{ \mathfrak{ \leadsto \: { \sf{x}} = \sqrt{81} }}$

$\displaystyle{ \mathfrak{ \leadsto \: \sf{x} = 9}}$

Hence, it's breadth measures 9 cm.