First, we will identify the data points we need to be able to find the area of the triangle.
the formula for the area of the triangle: height*opposite side / 2
Since it is a right triangle, we know that the straight sides are actually also the heights between each other, that is, the side that measures 5 and the side that measures 7.
We multiply the legs and divide by 2
25×7=235=17.5
Answer
17.5
Exercise #12
The triangle ABC is given below. AC = 10 cm
AD = 3 cm
BC = 11.6 cm What is the area of the triangle?
Video Solution
Step-by-Step Solution
The triangle we are looking at is the large triangle - ABC
The triangle is formed by three sides AB, BC, and CA.
Now let's remember what we need for the calculation of a triangular area:
(side x the height that descends from the side)/2
Therefore, the first thing we must find is a suitable height and side.
We are given the side AC, but there is no descending height, so it is not useful to us.
The side AB is not given,
And so we are left with the side BC, which is given.
From the side BC descends the height AD (the two form a 90-degree angle).
It can be argued that BC is also a height, but if we delve deeper it seems that CD can be a height in the triangle ADC,
and BD is a height in the triangle ADB (both are the sides of a right triangle, therefore they are the height and the side).
As we do not know if the triangle is isosceles or not, it is also not possible to know if CD=DB, or what their ratio is, and this theory fails.
Let's remember again the formula for triangular area and replace the data we have in the formula:
(side* the height that descends from the side)/2
Now we replace the existing data in this formula:
2CB×AD
211.6×3
234.8=17.4
Answer
17.4
Exercise #13
Triangle ABC is a right triangle.
The area of the triangle is 6 cm².
Calculate X and the length of the side BC.
Video Solution
Step-by-Step Solution
We use the formula to calculate the area of the right triangle:
2AC⋅BC=2cateto×cateto
And compare the expression with the area of the triangle 6
24⋅(X−1)=6
Multiplying the equation by the common denominator means that we multiply by 2
4(X−1)=12
We distribute the parentheses before the distributive property
4X−4=12 / +4
4X=16 / :4
X=4
We replace X=4 in the expression BC and
find:
BC=X−1=4−1=3
Answer
X=4, BC=3
Exercise #14
Calculate the area of the
triangle ABC given that its
perimeter equals 26.
Video Solution
Step-by-Step Solution
Remember that the perimeter of a triangle is equal to the sum of all of the sides together,
We begin by finding side BC:
26=9+7+BC
26=16+BC
We then move the 16 to the left section and keep the corresponding sign:
26−16=BC
10=BC
We use the formula to calculate the area of a triangle: