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Natasha_Volkova [10]
3 years ago
10

The height of the triangle is 7 cm longer than its base. the area of the triangle is 60 cm squared. what is the base of the tria

ngle?
Mathematics
2 answers:
gregori [183]3 years ago
8 0

Answer:

8 cm

Step-by-step explanation:

Let x cm be the length of the base, then the length of the height is x+7 cm. Use formula for the area of the triangle:

A_{triangle}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}

In your case,

60=\dfrac{1}{2}\cdot x\cdot (x+7),\\ \\120=x(x+7),\\ \\x^2+7x-120=0,\\ \\D=7^2 -4\cdot 1\cdot (-120)=49+480=529,\\ \\x_{1,2}=\dfrac{-7\pm\sqrt{529}}{2\cdot 1}=\dfrac{-7\pm 23}{2}=-15,\ 8

Since the base cannot have negative length, then x=8 cm.

Alenkasestr [34]3 years ago
3 0

<u>Answer:</u>

Base = 8 cm

<u>Step-by-step explanation:</u>

We are given that the height of a triangle is 7 cm longer than its base and its area is 60 cm squared.

We are to find the base of the triangle.

<em>Area of the triangle = \frac{1}{2} \times base \times height</em>

Assuming the base to be x, so height will be x+7

Substituting the values in the above formula to get:

60=\frac{1}{2} \times x \times (x+7)

120= x(x+7)

x^2+7x-120=0

Factorizing the quadratic equation to get:

x^2+15x-8x-120=0

x(x+15)-8(x+15)=0

(x-8)(x+15)=0

x = 8 and x = -15

Since base cannot be negative so it will be 8 cm.

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