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3 years ago

The area of a triangle is 10 cm2. Its base is 3 cm less than twice its height. What is the height of the triangle?

Mathematics

1 answer:

stiv31 [10]3 years ago

7 0

<h2>Answer:</h2><h2>The height of the triangle = 4cm</h2>

Step-by-step explanation:

Given, area of the triangle = 10 $cm^{2}$

Let the height of the triangle be h cm

Given, the base b is 3 cm less than twice its height.

b = 2h - 3 ... (1)

By formula, area of the triangle = $\frac{1}{2}$ bh .. (2)

substitute (1)in (2), we get

Area = $\frac{1}{2}$ (2h-3) h

10 = $\frac{1}{2}$ (2h-3) h

20 = $2h^{2} - 3h$

$2h^{2} - 3h$ - 20 = 0

solving the equation, we get x = 4, -2.5

The height of the triangle = 4cm

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Read 2 more answers

The length of a rectangle is 3 centimeters less than five times its width. Its area is 14 square centimeters. Find the dimension

inysia [295]

Answer:

The length of rectangle is 7 cm and width is 2 cm.

Step-by-step explanation:

Given that:

Area of rectangle = 14 square centimeters

The length of a rectangle is 3 centimeters less than five times its width.

Let,

L be the length and W be the width of the rectangle.

L = 5W - 3

Area of rectangle = Length * Width

14 = (5W-3)*W

$14=5W^2-3W\\5W^2-3W-14=0$

Factorizing the equation;

$5W^2-10W+7W-14=0\\5W(W-2)+7(W-2)=0\\(5W+7)(W-2)=0$

Either,

5W+7 = 0

5W = -7

W = -7/5

Or,

W-2 = 0

W=2

As width of rectangle cannot be negative, therefore,

Width = 2 centimeters

Length = 5(2) -3 = 10-3 = 7

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The length of rectangle is 7 cm and width is 2 cm.

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3 years ago