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3 years ago

The altitude of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find its base and altitude.

Mathematics

1 answer:

zavuch27 [327]3 years ago

8 0

9514 1404 393

Answer:

base: 12 in

altitude: 7 in

Step-by-step explanation:

The formula for the area of a triangle is ...

A = 1/2bh

Filling in the given information, we have ...

42 = 1/2(b)(b -5)

b^2 -5b -84 = 0 . . . . multiply by 2, put in standard form

(b -12)(b +7) = 0 . . . . factor

The only positive solution is b = 12

The base is 12 inches; the altitude is 7 inches.

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3 years ago

Read 2 more answers

The length of a rectangle is 8 feet more than its width. If the width is increased by 4 feet and the length is decreased by 5 fe

bezimeni [28]

Assign the following variables for the origina3l rectangle:
let w = width let w + 8 = length and the area would be w(w + 8) = w² + 8w

No for the second rectangle:
let (w + 4) = width and (w + 8 - 5) or (w + 3) = length
Area = length x width or (w + 4)(w + 3) = w² + 3w + 4w + 12 using the foil method to multiply to binomials. Simplified Area = w² + 7w + 12

Now our problem says that the two area will be equal to each other, which sets up the following equation:

w² + 8w = w² + 7w + 12 subtract w² from both sides
8w = 7w + 12 subtract 7w from both sides
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3 years ago

Solve for the variable a D =a+b-c/3

yuradex [85]

Hey there,
solving for a is just like you think of all other letter as a constant
i.e the only variable is a
so you need to subtract b as a start
d=a+b-c/3
-b -b
=============

-b+d=a-c/3 now it's time to add c/3 (isolate a by itself in one side)

-b+d=a-c/3
+c/3 +c/3
==============
c/3-b+d=a

Hence you have solved for a

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4 years ago

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3 years ago

A water tower casts a 100-foot shadow. At the same time, an 8-foot stri

bogdanovich [222]

Set up ratios of height / shadow length:

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3 years ago

The altitude of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find its base and altitude.​

The altitude of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find its base and altitude.