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3 years ago

A right triangle's height is 3 times the length of its base. if the area of the triangle is 486, what is the height?

1 answer:

4 0

The formula of the area of a triangle:
$A_\Delta=\dfrac{bh}{2}$
b - the bash - the height
We have:
b - the base3b - the height486 - the area

Substitute:
$\dfrac{3b\cdot b}{2}=486\ \ \ |\cdot2\\\\3b^2=972\ \ \ |:3\\\\b^2=324\to b=\sqrt{324}\\\\b=16\to h=3b=3\cdot18=54$
Answer: The length of the height is equal 54 units.

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3 years ago

the length of a rectangle is 5 times as long as its breadth and its area is 1620 m² find area of square whose perimeter is equal

Rus_ich [418]

Answer:

Area of the square is 2916 $m^{2}$ .

Step-by-step explanation:

Let the breadth of the rectangle be represented by w. So that;

length of rectangle = 5w

Area of rectangle = length x breadth

= 5w x w

1620 = 5 $w^{2}$

divide through by 5 to have,

$w^{2}$ = 324

w = $\sqrt{324}$

= 18

Thus, the breadth of the rectangle is 18 m.

length = 5 w = 5 x 18

= 90 m

The length of the rectangle is 90 m.

Perimeter of the rectangle = 2(l + w)

= 2( 90 + 18)

= 216 m

Perimeter of a square = 4l

where l is the length of its side.

Given that the perimeters of the rectangle and square are equal, then;

4l = 216

l = $\frac{216}{4}$

= 54

length of the side of square is 54 m.

Therefore,

Area of square = $l^{2}$

= $54^{2}$

= 2916

Area of the square whose perimeter is equal to that of the rectangle is 2916 $m^{2}$ .

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3 years ago