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2 years ago

Find the area of each figure. Round to the nearest hundredth where necessary.

Mathematics

1 answer:

Papessa [141]2 years ago

3 0

Answer:

The answer to your question is Triangle's area = 520 in², Square's area = 576 in²

Step-by-step explanation:

Process

1.- Calculate the area of the triangle

-Find the length of the base using the Pythagorean theorem

c² = a² + b²

-Solve for b²

b² = c² - a²

-Substitution

b² = 37² - 35²

-Simplification

b² = 1369 - 1225

b² = 144

b = 12 in

-Find the base

base = 2(12) = 24 in

-Find the area of the triangle

Area = base x height / 2

-Substitution

Area = 24 x 35 / 2

-Simplification

Area = 420 in²

2.- Find the area of the square

Area = side x side

-Substitution

Area = 24 x 24

-Result

Area = 576 in²

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2 years ago

Ray has found that his new car gets 31 miles per gallon on the highwayand 26 miles per gallon in the city. He recently drove 285

Mkey [24]

Answer:

$Highway = 155\ miles$

$City = 130\ miles$

Step-by-step explanation:

Given

$Highway = 31mi/gallon$

$City = 26mi/gallon$

$Total\ Miles = 285$

$Total\ Gallons = 10$

Required

Determine the number of miles driven on the highway and on the city

Represent the gallons used on highway with h and on city with c.

So, we have:

$c + h = 10$ ---- gallons used

and

$31h + 26c = 285$ --- distance travelled

In the first equation, make c the subject

$c = 10 - h$

Substitute 10 - h for c in the second equation

$31h + 26c = 285$

$31h + 26(10 - h) = 285$

Open bracket

$31h + 260 - 26h = 285$

Collect like terms

$31h - 26h = 285 - 260$

$5h = 25$

Make h the subject

$h = \frac{25}{5}$

$h = 5$

Substitute 5 for h in $c = 10 - h$

$c = 10 - 5$

$c = 5$

If on the highway, he travels 31 miles per gallon, then his distance on the highway is:

$Highway = 31 * 5$

$Highway = 155\ miles$

If in the highway, he travels 26 miles per gallon, then his distance on the highway is:

$City = 26 * 5$

$City = 130\ miles$

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2 years ago