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zlopas [31]
3 years ago
15

Se tiene un rectángulo cuya base mide el doble que su altura y su área es 12

Mathematics
1 answer:
irina [24]3 years ago
3 0

Answer:

Part 1) The perimeter is  P=6\sqrt{6}\ cm

Part 2) The diagonal is d=\sqrt{30}\ cm

Step-by-step explanation:

<u><em>The question in English is</em></u>

You have a rectangle whose base is twice the height and its area is 12

square centimeters. Calculate the perimeter of the rectangle and its diagonal

step 1

Find the dimensions of rectangle

we know that

The area of rectangle is equal to

A=bh

A=12\ cm^2

so

bh=12 ----> equation A

The base is twice the height

so

b=2h ----> equation B

substitute equation B in equation A

(2h)h=12\\2h^2=12\\h^2=6\\h=\sqrt{6}\ cm

Find the value of b

b=2\sqrt{6}\ cm

step 2

Find the perimeter of rectangle

The perimeter is given by

P=2(b+h)

substitute

P=2(2\sqrt{6}+\sqrt{6})\\P=6\sqrt{6}\ cm

step 3

Find the diagonal of rectangle

Applying the Pythagorean Theorem

d^2=b^2+h^2

substitute

d^2=(2\sqrt{6})^2+(\sqrt{6})^2

d^2=30

d=\sqrt{30}\ cm

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