In a rectangle diagonal is 5cm ,breadth is 3cm .find the area and perimeter of the rectangle? (STEP BY STEP EXPLANATION)

Mathematics

1 answer:

DerKrebs [107]3 years ago

3 0

Answer:

The area of rectangle is 12cm² and the perimeter is 14cm.

Step-by-step explanation:

First, you have to find the length of the rectangle using Pythagoras Theorem :

a² + b² = c²

a² + 3² = 5²

a² = 5² - 3²

a² = 16

a = √16

a = 4 cm

Next, you have to find the perimeter and area of rectangle :

Perimeter = 2(length + breadth)

P = 2(4 + 3)

P = 2(7)

P = 14 cm

Area = length×breadth

A = 4×3

A = 12 cm²

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2 years ago

PLEASE HELP ME thank you<br><br> answer needs to be in simplest radical form <br><br> find d

sweet [91]

Answer:

$d=10$

Step-by-step explanation:

Pythagorean theorem:

$d^2+d^2=10\sqrt{2}^2,\\2d^2=200,\\d^2=100,\\d=\boxed{10}$

Alternative:

$\cos 45^{\circ}=\frac{d}{10\sqrt{2}},\\\frac{\sqrt{2}}{2}=\frac{d}{10\sqrt{2}},\\2d=10\sqrt{2}\cdot \sqrt{2},\\2d=20,\\d=\boxed{10}$

Alternative (derived from the Pythagorean theorem):

All 45-45-90 triangles have side lengths $x-x-x\sqrt{2}$ , where $x\sqrt{2}$ is the hypotenuse. Since this triangle's hypotenuse is $10\sqrt{2}$ , its sides are $10-10-10\sqrt{2}$ .