Step-by-step explanation:
Q12.
I checked immediately : 33 m, 44 m and 55 m create a right-angled triangle, as they satisfy the Pythagoras rule :
c ² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle) and longer than the legs, and a and b being the legs of the triangle.
55² = 33² + 44²
3025 = 1089 + 1936 = 3025
correct.
the area of a triangle is
baseline × height / 2
in case of a right-angled triangle we can use the right angle situation, the legs are acting as baseline and height (due to the 90° angle between them).
and so the area of the triangle here is
A = 33×44/2 = 33×22 = 726 m²
as 1 m² costs 1.20 per m², we have a total costs
1.20 × 726 = 871.2
for the second part of the question :
again the area of a triangle is
baseline × height / 2
baseline is tripled and height is doubled.
that means compared to the original sizes the are is now ;
(baseline × 3) × (height × 2) / 2 =
= 3×2 × baseline × height / 2 = 6 × baseline × height / 2
the area of the new triangle is their 6 time the area of the original triangle.
Q16
5th root of (243a¹⁰b⁵c¹⁰)
remember, when we have exponent of exponent, we multiply the exponents. and an nth root is nothing else than the exponent 1/n.
and the higher level exponent has to be applied to all factors of the lower level exponent.
so, we have
243^(1/5) × a^(10 × 1/5) × b^(5 × 1/5) × c^(10 × 1/5) =
3 × a² × b¹ × c² = 3a²bc²
Q19.
it is a right-angled triangle, and it is isoceles. that means both legs (they contain between themselves the 90° angle) are equally long.
the area is again
baseline × height / 2.
and again, the legs are acting as baseline and height.
so,
8 = leg × leg / 2 = leg²/2
leg² = 16
leg = 4 cm
both legs are 4 cm.
now we use Pythagoras to get the missing side (Hypotenuse) :
Hypotenuse² = leg² + leg² = 16 + 16 = 32 = 2×16
Hypotenuse = sqrt(2×16) = 4×sqrt(2) cm
for the second part of the question :
this means
one leg of the triangle is 8 cm. for the Hypotenuse we have 10 cm.
now we can apply Pythagoras again :
10² = 8² + leg²
100 = 64 + leg²
36 = leg²
leg = 6 cm
so its area is
A = 6 × 8 / 2 = 6 × 4 = 24 cm²
