Answer:
15cm by 20cm by 25cm
Step-by-step explanation:
Let the sides of the right angle be x, y and h
x is the breadth
y is the height
h is the hypotenuse
Perimeter = x + y + h
x + y +h = 60
x+y = 60-h .... 1
If its area is equal to 150 square cm, then;
Area = 1/2 * base * height
Area = 1/2 *x * y
xy/2 = 150
xy = 300 ....2
According to pythagoras theorem;
x² + y² = h²
On expanding x² + y²
x² + y² = (x+y)² - 2xy
The equation becomes
(x+y)² - 2xy = h² ... 3
Substitute equation 1 and 2 into 3;
From 3;
(x+y)² - 2xy = h² ... 3
(60-h)² - 2(300) = h²
3600-120h + h² - 600 = h²
3600-120h - 600 = 0
-120h = 600-3600
-120h = -3000
h = 3000/120
h = 25cm
Recall that x+y+h = 60
x+y+25 = 60
x+y = 60 - 25
x+y = 35 ... 4
From equation 2;
xy = 300
x = 300/y ..... 5
Substitute 5 into 4;
300/y + y = 35
(300+y²)/y = 35
300+y² = 35y
y²-35y + 300 = 0
y²-20y-15y + 300 = 0
y(y-20)-15(y-20) = 0
y-20 = 0 and y - 15 =0
y = 20 and 15
since x+y = 35
x + 20 = 35
x = 35 - 20
x = 15
Hence the sides of the triangle are 15cm by 20cm by 25cm
Answer:
10cm
Step-by-step explanation:
the formula for an area of a trapezium:
where a and b are the parallel sides and h is the height. equating what we have:
simplify the numerator by adding 19.8 and 7.2=27
multiply both sides by 2
divide both sides by 27
the height is 10cm
The building would have to be 24 feet tall
36 inch is 3 ft
21/3=7
168/7=24
Step-by-step explanation:
A better way to word this is how much more is 4/9 than 2/9 which is 2/9 more because 2/9 plus 2/9 is 4/9 and the denominator stays the same
Answer:
x ≤ 3
Step-by-step explanation:
The vertical line at x = 3 is solid and shaded to the left
Therefor
x ≤ 3
