Respuesta :

frika

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:

[tex]A_{triangle}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}[/tex]

In your case,

[tex]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[/tex]

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

alinakincsem

Answer:

Base = 8 cm

Step-by-step explanation:

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.

Area of the triangle = [tex]\frac{1}{2} \times base \times height[/tex]

Assuming the base to be [tex]x[/tex], so height will be [tex]x+7[/tex]

Substituting the values in the above formula to get:

[tex]60=\frac{1}{2} \times x \times (x+7)[/tex]

[tex]120= x(x+7)[/tex]

[tex]x^2+7x-120=0[/tex]

Factorizing the quadratic equation to get:

[tex]x^2+15x-8x-120=0[/tex]

[tex]x(x+15)-8(x+15)=0[/tex]

[tex](x-8)(x+15)=0[/tex]

[tex]x = 8[/tex] and [tex]x = -15[/tex]

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

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