The front of an a-frame cabin in a national park is in the shape of a triangle, with an area of 248 ft. if the height is 1 ft less than twice the base, find the base and the height of the front of the cabin.

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The front of an a-frame cabin in a national park is in the shape of a triangle, with an area of 248 ft. if the height is 1 ft less than twice the base, find the base and the height of the front of the cabin.

Socrat use det app ok

the length of o'p' is [tex]1.5\times op[/tex].

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

[tex]k=\frac{o'p'}{op}[/tex]

the scale factor is 1.5.

[tex]1.5=\frac{o'p'}{op}[/tex]

multiply both sides by op.

[tex]1.5\times op=o'p'[/tex]

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is [tex]1.5\times op[/tex].

Area of triangle=1/2bh

Area=248ft

Base=x

Height=2x-1

248=1/2×x×(2x-1)